Balancing Matching of Two-Sided Agents with Adaptive and Fair Instability
Bibliographic record
Abstract
The concept of stable matching is substantially used in bipartite graphs with individual preferences of the vertices. The existence of stability restricts the weight and size of the matching to be satisfactory. We study the trade-offs in stability, weight and cardinality in a one-to-many capacitated weighted bipartite matching with an edge-weight-oriented preference setting. We establish a stability relaxation framework which is adaptive to the pairing suitability and capacity of the vertices. The purpose of the relaxation is to update the stable matching towards the balance of stability, weight and cardinality in the result. The relaxation preserves fairness by keeping the satisfaction degradation of the vertices with the potential new partner in a desired range. We propose an algorithm to produce a new matching using the stability relaxation framework. Furthermore, we define a novel popularity measurement model of matching based on the edge weight with the multi-voting ability of one-sided vertices. We show the resulting matching is also popular as stable matching. The experimentation performed based on the use case of the homeless placement system complements the claim of improving the weight and cardinality in the matching with marginal and fair relaxation of stability.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".